Determining How Costs
Behave
Dr. Hisham Madi
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Cost Estimation Methods
The industrial engineering method,
 This is also called the work-measurement method, estimates
cost functions by analyzing the relationship between inputs and
outputs in physical terms.
 This is a thorough and detailed method, but can be very timeconsuming.
 For example, a carpet manufacturer that uses inputs of cotton,
wool, dyes, direct labour, machine time and power. Production
output is square metres of carpet
 Time-and-motion studies analyse the time and materials required
to perform the various operations to produce the carpet
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Cost Estimation Methods
 A time-and-motion study may conclude that to produce 20 square
metres of carpet requires 2 kilograms of cotton and 3 litres of dye
 The result is an estimated cost function relating total
manufacturing costs to the cost driver, square metres of carpet
 Many organizations, however, find it too costly for analyzing
their entire cost structure.
 More frequently, organizations use this approach for direct-cost
categories such as materials and labour but not for indirect-cost
categories such as manufacturing overhead

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Cost Estimation Methods
Conference method
 The conference method estimates cost functions on the basis
of analysis and opinions about costs and their drivers gathered
from various departments of an organization (purchasing,
process engineering, manufacturing, employee relations, and so
on)
 Because it does not require detailed analysis of data, it can be
used to develop cost functions very quickly.
 However, the emphasis on opinions rather than systematic
estimation can make this a less accurate method.
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Cost Estimation Methods
Account analysis method
The account analysis method estimates cost functions by
classifying various cost accounts as variable, fixed, or mixed with
respect to the identified level of activity.
Consider indirect manufacturing labour costs for a small
production area (or cell) at Møre-Teppe.
These costs include maintenance, quality control and set-up
costs for the machines
Møre-Teppe worked the machines in the cell for a total of 862
hours and incurred total indirect manufacturing labour costs of
€12 501
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Cost Estimation Methods
 Management wants the cost analyst to use the account analysis
method to estimate a linear cost function for indirect
manufacturing labour costs with machine-hours as the cost
driver.
 The
cost analyst decides to separate total indirect
manufacturing labour costs (€12 501) into costs that are fixed
(€2157) and costs that are variable (€10 344) with respect to
the number of machine-hours worked
 Variable costs per machine-hour are €10 344 ÷ 862 = €12.
 The general cost equation, y = a + bX, is indirect
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manufacturing labour costs = €2157 + (€12 × number of
machine-hours). The indirect manufacturing labour cost per
machine-hour is €12 501 ÷ 862 = €14.50.
Cost Estimation Methods
 Management at Møre-Teppe can use the cost function to
estimate the indirect manufacturing labour costs of using 950
machine-hours to produce carpet in the next 12 week period.
 Using the cost function, estimated costs = €2157 + (950 × 12) =
€13 557.
 The indirect manufacturing labour costs per machine-hour
decrease to €13 557 ÷ 950 = €14.27,
 Organizations must take care to ensure that individuals
thoroughly knowledgeable about the operations make the costclassification decisions, to obtain reliable estimates of the fixed
and variable components of cost
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Cost Estimation Methods
Quantitative Analysis Method
 The quantitative analysis method uses formal mathematical models to fit
cost functions to past data observations. The most common quantitative
analysis methods are the high-low method and regression analysis.
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Steps in estimating a cost function Using Quantitative
Analysis
Step 1 Choose the dependent variable (cost being estimated or
predicted). The dependent variable is the cost being
estimated (y in the equation) and depends on the cost
function being estimated.
For example,
 if the purpose is to determine indirect manufacturing costs for a
production line, then the dependent variable should incorporate
all costs that are classified as indirect with respect to the
production line
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Steps in estimating a cost function Using
Quantitative Analysis
Step 2 Identify the independent variable, or cost driver. The
independent variable is the factor used to predict the cost
function.
 This is the cost driver, otherwise referred to as X in the
equation, or the slope.
 The cost driver should be measurable and have an cause-effect
relationship to the dependent variable.
 Consider several types of fringe benefit paid to employees and
their cost drivers:
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Steps in estimating a cost function Using Quantitative
Analysis
 The costs of health benefits and cafeteria meals can be
combined into one cost pool because they both have the same
cost driver, number of employees. Pension benefits and life
insurance costs have a different cost driver, salaries of
employees
Step 3 Collect data on the dependent variable and the cost
driver. This is usually the most difficult step, as the data
comes from a number of sources, and managers need to be
concerned about the validity of the data
 Time-series data pertain to the same entity (organisation, plant,
activity area, and so on) over a sequence of past time periods
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Steps in estimating a cost function Using Quantitative
Analysis
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
Weekly observations of indirect manufacturing labour costs and machinehours in the Møre-Teppe illustration are an example of time-series data.

The ideal time-series database would contain numerous observations for a
firm whose operations have not been affected by economic or technological
change.

Stable technology ensures that data collected in the estimation period
represent the same underlying relationship between the dependent variable
and the cost driver

Cross-sectional data pertain to different entities for the same time period.

For example, studies of personnel costs and loans processed at 50 individual
branches of a bank during March would produce cross-sectional data for
March.
Steps in estimating a cost function Using Quantitative
Analysis
Step 4 Plot the data. By plotting the data on a scattergraph it can
be determined if a linear relationship exists. Also, this alerts
the manager to any extreme observations.
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Steps in estimating a cost function Using Quantitative
Analysis
 Plotting the data can also provide insight into whether the
relation is approximately linear and what the relevant range of
the cost function is.
Step 5 Estimate the cost function. As mentioned, there are two
primary methods of estimating a cost function—the high-low
method and regression analysis.
 By using the high–low method and regression analysis
Step 6 Evaluate the cost driver of the estimated cost function
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High–low method
 Managers, at times, use very simple methods to estimate cost
functions.
 Using only the highest and lowest observed values of the cost
driver within the relevant range.
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High–low method
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High–low method
 To compute the constant, we can use either the highest or the
lowest observation of the cost driver.
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High–low method
Advantages of the high-low method are that it is simple to compute
and understand, and it can give a quick insight into cost-activity
relationships. However, it utilizes only two data points, thus
ignoring a great deal of valid data.
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Regression analysis method
 Regression analysis is a statistical method that measures the
average amount of change in the dependent variable that is
associated with a unit change in one or more independent
variables.
 Simple regression analysis estimates the relationship between
the dependent variable and one independent variable.
 Multiple regression analysis estimates the relationship between
the dependent variable and multiple independent variables
 Regression analysis is widely used because it helps managers
understand why costs behave as they do and what managers can
do to influence them
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Regression analysis method
 The difference between actual and predicted cost is called the
residual term
 The smaller the residual terms, the better the fit between
predicted costs and actual cost observations
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Regression analysis method
 Goodness of fit indicates the strength of the relationship between
the cost driver and costs
Y = €300.98 + €10.31X
 The estimate of the slope coefficient b indicates that the average
indirect manufacturing labour costs vary at the rate of €10.31 for
every machine-hour within the relevant range.
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Evaluating and choosing Cost Drivers
 How does a company determine the best cost driver when
estimating a cost function?
 Is this the best cost driver to predict the behavior?
 How good is this driver at predicting cost behavior?
 Suppose Møre-Teppe wants to evaluate whether direct
manufacturing labour-hours is a better cost driver than
machine-hours for indirect manufacturing labour costs.
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Evaluating and choosing Cost Drivers
There are three criteria often used to evaluate cost drivers; they are:
 Economic plausibility. Do the cost driver and the level of costs
seem to be related? Does it make sense that an increase in the
independent variable will cause an increase in the costs?
 Highly automated production environment of Møre-Teppe, costs
are likely to be more closely related to machine-hours than to direct
manufacturing labour-hours.
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Evaluating and choosing Cost Drivers
 Goodness of fit. Are the differences between the actual costs and
predicted costs small? In a regression analysis, goodness of fit is
measured by the r2 statistic.
 The vertical differences between actual and predicted costs are
much smaller for machine-hours than for direct manufacturing
labour-hours – machine-hours has a stronger relationship with
indirect manufacturing labour costs.

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Evaluating and choosing Cost Drivers
 Significance of independent variable. If the regression line (or
total cost line) has a steep slope, this indicates a strong
relationship between the cost driver and the costs incurred
 The machine-hours regression line has a relatively steep slope
while the direct manufacturing labour-hours regression line is
relatively flat (small slope)
 A relatively flat regression line indicates a weak or no relationship
between indirect manufacturing labour costs and direct
manufacturing labour-hours.
 On average, changes in direct manufacturing labour-hours appear
to have a minimal effect on indirect manufacturing labour costs.
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Evaluating and choosing Cost Drivers
Why is choosing the correct cost driver to estimate indirect
manufacturing labor costs important?
 Because identifying the wrong drivers or misestimating cost functions can
lead management to incorrect (and costly) decisions
 Management estimates 72 machine-hours and 21 direct manufacturing laborhours would be required per week to produce new style of carpet.
Machine-hours as the cost driver
 Cost function y= €300.98 + (€10.31 ×machine-hours) to predict future
indirect manufacturing labour costs
 Using this model, Møre-Teppe would predict costs of y=€300.98 +(€10.31
×72) = €1043.30
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Evaluating and choosing Cost Drivers
labour-hours as the cost driver
 Predicted cost is €744.67 + (€7.72 ×21) = €906.79
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Cost drivers and Activity-Based Costing
 Estimating cost drivers in an activity-based costing system
doesn’t differ in general from what’s been discussed.
 However, since ABC systems have a great number and variety of
cost drivers and cost pools, managers must estimate many cost
relationships.
 In estimating the cost function for each cost pool, the manager
must pay careful attention to the cost hierarchy.
 For example, if a cost is a batch-level cost such as setup cost, the
manager must only consider batch-level cost drivers like number
of setup-hours.
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Cost drivers and Activity-Based Costing
 ABC systems emphasise long-run relationships between the cost
driver (level of activity) and cost.
 Because in the short run, costs may be fixed and, therefore, will
not vary with changes in the level of the cost driver
 The long-run focus means that more costs are variable, which
leads to a stronger cause-and-effect relationship between the cost
driver and the corresponding cost
 Hence, the ideal database to estimate cost driver rates will
contain data over a longer time period
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Cost drivers and Activity-Based Costing
 If the time period used to estimate the cost relationship is short,
the relationship between changes in the cost driver and changes
in cost may be weak. Why
 Because many costs are acquired in lump-sum amounts and
hence are fixed in the short run while the levels of activity vary.
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Nonlinear Cost Functions
 cost functions are not always linear.
 A non-linear cost function is a cost function where, within the
relevant range, the graph of total costs versus the level of a single
activity is not a straight line
 Some examples of nonlinear cost functions follow
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Nonlinear Cost Functions
Economies of scale
 Direct materials costs are not always linear variable costs.
 Consider quantity discounts on direct materials purchases.
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Nonlinear Cost Functions
 the total direct materials costs rise, but they rise more slowly as
the cost driver increases because of quantity discounts
 b= €25 for 1–1000 units purchased; b = €15 for 1001–2000
units purchased; and b= €10 for 2001 or more units purchased
(a= €0 for all ranges of the units purchased).
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Nonlinear Cost Functions
A step cost function
 is a cost function in which the cost is constant over various ranges
of the cost driver, but the cost increases by discrete amounts (that
is, in steps) as the cost driver moves from one range to the next.
 A step variable-cost function, a step cost function in which cost is
constant over narrow ranges of the cost driver in each relevant
range.
 The pattern is a step cost function because set-up costs are
incurred only when each production batch is started
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Nonlinear Cost Functions
Learning curve
 A function that measures how labor-hours per unit decline as
units of production increase because workers are learning and
becoming better at their jobs.
 Managers use learning curves to predict how labour-hours (or
labour costs) will change as more units are produced
 The aircraft-assembly industry first documented the effect that
learning has on efficiency. As workers become more familiar
with their tasks, their efficiency improves.
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Nonlinear Cost Functions
Learning curve
 Managers are now extending the learning-curve notion to include
other cost areas in the value chain, such as marketing,
distribution and customer service
 An experience curve is a function that shows how full product
costs per unit (including manufacturing, marketing, distribution,
and so on) decline as units of output increase.
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Types of Learning Curves
 Cumulative average time per unit declines by a constant
percentage each time the cumulative quantity of units produced
doubles.
 Rayburn has an 80% learning curve.
 The 80% means that when the quantity of units produced is
doubled from X to 2X, cumulative average time per unit for
2Xunits is 80% of cumulative average time per unit for X units.
Average time per unit has dropped by 20% (100% – 80%).
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Types of Learning Curves
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Types of Learning Curves
Incremental Unit-Time Learning Model
 Incremental time needed to produce the last unit declines by a
constant percentage each time the cumulative quantity of units
produced doubles.
 80% learning curve
 The 80% here means that when the quantity of units produced is
doubled from X to 2X, the time needed to produce the last unit
when 2Xtotal units are produced is 80% of the time needed to
produce the last unit when X total units are produced
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Types of Learning Curves
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Types of Learning Curves
 The incremental unit-time learning model predicts a higher
cumulative total time to produce 2 or more units than the
cumulative average-time learning model,
 assuming the same learning rate for both models 80%.
 If we compare the results, to produce 4 cumulative units,
 the 80% incremental unit-time learning model predicts 314.21
labor-hours versus 256.00 labor-hours predicted by the 80%
cumulative average-time learning model.
 That’s because under the cumulative average-time learning
model average labor-hours needed to produce all 4 units is 64
hours; the labor-hour amount needed to produce unit 4 is
much less than 64 hours—it is 45.37 hours
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Types of Learning Curves
 Under the incremental unit-time learning model, the laborhour amount needed to produce unit 4 is 64 hours, and the laborhours needed to produce the first 3 units are more than 64 hours,
so average time needed to produce all 4 units is more than 64
hours
 How do managers choose which model and what percent
learning curve to use?
 Engineers, plant managers, and workers are good sources of
information on the amount and type of learning actually
occurring as production increases
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Predicting Costs Using Alternative Time Learning Models
How do companies use learning curves?
 For example, a company might set an extremely low selling price
on its product in order to generate high demand.
 As the company’s production increases to meet this growing
demand, costs per unit drop.
 The company rides the product down the learning curve as it
establishes a higher market share.
 Although the company may have earned little on its first unit sold
– it may actually have lost money – the company earns more
profit per unit as output increases
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Predicting Costs Using Alternative Time Learning Models
Alternatively,
 the company might set a low price on just the final 8 units. After
all, the labour and related overhead costs per unit are predicted to
be only€12 288 for these final 8 units (€32 768 – €20 480).
 The per unit costs of €1536 on these final 8 units (€12 288 ÷ 8)
are much lower than the €5000 costs per unit of the first unit
produced.
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